"Rules that preserve structure even after transformation" "Operation of symmetry" Finite simple group classification theorem (Classification of Finite Simple Groups) sporadic = sporadic, isolated 「説明不能な秩序」 Mathematical Architecture space "If you like this architectural artwork, you can purchase the high-resolution digital file [here on Payhip (https://payhip.com/MathematicalArchitectureS)] or [here on Gumroad (https://shomei.gumroad.com/l/apmao)]."

(An energetic perspective) Energy (Hamiltonian) → Time evolution → Motion There is an "invisible topography (energy undulation)" in space, and particles flow through it. "Architecture that designs movement itself" 動いていないのに動いて見える "Dynamic Space Architecture" Mathematical Architecture space ■ Gumroad https://shomei.gumroad.com/l/apmao ■ Lemon Squeezy https://shomei.lemonsqueezy.com/ ■ Payhip https://payhip.com/MathematicalArchitectureS ■ BOOTH https://shomei-a.booth.pm

They may look different, but their relationship structure is the same. Two spaces exist: A: Physical space (visible architecture) wall floor volume light B: Relational space (invisible architecture) Traffic flow network Eye contact Sound propagation Function links Space becomes "doubled" 「空間ではなく、空間同士の関係を設計し、それが別の幾何として現れる建築」 "Visible architecture" and "invisible architecture" Mathematical Architecture space

"The smallest unit of finite symmetry that cannot be further decomposed." "Symmetry like that of 'elementary particles' in a finite world" → Finite simple group = "Prime number" in the world of groups Finite simple group = symmetric atom The concept of a room disappears. There is no hallway Structure and traffic flow are integrated. ① You get lost (but it's not broken) → The symmetry is so strong that you lose your sense of direction. ② No center → Everything feels like the c

Mathematics that goes as far as "the relationship of the relationship of the relationship..." "Relationships are more important than material things." dimension Content 0 subject 1 Relationship of the subject 2 Relationship 3 Relationship of relationships n Infinite Layers The most abstract theory → A universe where structures are stacked hierarchically. 多層ネットワーク空間建築 Symplectic → “The geometry of motion” Mathematical Architecture space

"Architectural design generated using probability and randomness" Buildings = Topography of probability distributions → Topographication Order × Randomness = Statistical Order 臨界状態（壊れる一歩手前） (Space becomes distorted) A space where a continuous function appears discontinuous → The architectural representation of phenomena Mathematical Architecture space

"Geometric spaces with completely different shapes actually contain the same information." Space A Space B Geometry: Counting Curves Geometry for studying hole structure Space A Space B (Complex curve) ←→ (Complex hole) 鏡宇宙を移動する体験 Twin buildings with different shapes Architecture A Architecture B Organic forms full of curves linear Flowing Corridor Courtyard type Movement distance, line of sight, and spatial volume are in perfect agreement. Mathematical Architecture space

Mathematics that deals with "shape (topology)" and "logic/programs" in the same language. Space = Transformable proof → Architecture that allows you to walk through a proof → Architecture that is a maze yet leads you to the same place ∞次元トポロジー Mathematics = multidimensional space → Loops, twists, non-Euclidean wires Mathematical Architecture space

"A phenomenon where seemingly unrelated fields of mathematics coincide at an unbelievable level." Monstrous Moonshine The coefficients in the expansion of the modular function are as follows: 196884 = 196883 + 1 196883 → Dimensions of representation of monster groups 1 → Self-evident expression "Architecture where structure and light are perfectly aligned" 広大な都市広場の中央に、完全に無機質な黒い直方体が静かに立っている。 The surface appears flat at first glance, but upon closer inspection, countless irregu

A structure in which countless circles within a 3-dimensional sphere correspond neatly to a 2-dimensional sphere. "A space created by the intertwining of infinite circular corridors." ”思考スタイル”として再構成した比較想像図 ① Flowing curved surface type ② Silent minimalist type ③ Structural logic exposed type Fluid / Continuous / Dynamic Geometry 迷路ではなく流体空間 Mathematical Architecture space

An equation that smooths out the "curvature" of space over time. Imagine this: → There's a wrinkled surface → We'll make the shape uniform. → Something like heat diffusion in space → Smooths out curvature → Deforms the shape of space over time → Shape evolves → Space becomes simpler → Shape becomes smoother over time → “Chaos → Order” A monumental cultural hall inspired by Ricci Flow geometry, aerial drone perspective, the architecture expresses a continuous transformation f

A concept of urban design that applies random movement to urban forms, probabilistically generated curved cities normal city + + + + + + + + + + + + + + + Brown City ~ ~ ~~ ~ ~~ ~ ~~ ~~~ Cities are "generated like terrain." ground Gentle, random undulations road No straight lines It continues to curve slightly. building Embedding in a curved surface In other words City = Mega-landscape parametric city 「ブラウン多様体都市」 The space itself is a performance device; the cross-section is

Shapes that cannot be explained in ordinary dimensions (1D, 2D, 3D) Famous dimension ① Koch curve Dimensions: Approximately 1.26 dimensions ② Sierpinski triangle Dimensions: Approximately 1.58 dimensions ③ Cantor set Dimensions: Approximately 0.63 dimensions "Architecture where scale collapses" 建物 ≒ 地形 ≒ 宇宙構造 Prompt 1 fractal architecture based on Hausdorff dimension, recursive self-similar structure, infinite detail facade, multi-scale geometry, organic yet mathematical form

"Infinity has varying degrees of magnitude." Cantor Dust fractal topology infinite structure All of these originate from Cantor's set theory. "A city that exists, yet hardly exists." 「都市を削ることで現れる都市」 Cantor Group Mathematical Architecture space